I think the biggest thing that can move this whole thing forward would be if you and the GF can work on your own relationship. If you don't connect sexually - that's ok. But you ARE sharing something and that can be something that can bring you together.
The topic of conversation doesn't always have to be about the relationship - and shouldn't. Both being the same gender you probably have quite a few things in common about your life in general you might connect on.
The better friends you can become the more smoothly the whole thing will flow.